Question

1. Explain why n root a^n= |a| when n is even, but not when n is odd.

Answer 1

Explanation:

In the expression a^n, for integer values of n greater than 1, there are n factors. For example, a^2 = a * 2 (2 factors), a^3 = a * a * a (3 factors), etc.

For a non-negative value of a, a^n is non-negative for all values of n.

If a is negative, and n is even, then a^n is non-negative.

If a is negative, and n is odd, then a^n is negative.

|a| is non-negative for all values of a.

sqrt_n(a^n) is negative for negative a and odd n, but |a| is always non-negative, so sqrtn(a^n) cannot equal |a| for odd n.